We consider the situation when an elliptic problem in a subdomain Ω1 of an n-dimensional bounded domain Ω is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in Ω∖Ω1. In particular, we can treat elliptic-parabolic equations in bounded domains with discontinuous coefficients. Using Fourier multiplier techniques, we prove an a priori estimate for strong solutions to the equations in Lp-Sobolev spaces.

We consider the situation when an elliptic problem in a subdomain Ω<sub>1</sub> of an n-dimensional bounded domain Ω is coupled via inhomogeneous canonical transmission conditions to a parabolic problem in Ω∖Ω<sub>1</sub>. In particular, we can treat elliptic-parabolic equations in bounded domains with discontinuous coefficients. Using Fourier multiplier techniques, we prove an a priori estimate for strong solutions to the equations in L<sup>p</sup>-Sobolev spaces.Denk, Robert2014Seger, TimSeger, TimengL<sup>p</sup>-estimates for a transmission problem of mixed elliptic-parabolic type2014-06-13T07:14:29ZBoundary value problems ; (2014). - 22deposit-license2014-06-13T07:14:29ZDenk, Robert